论文标题
在弱的ARF $（S_2）$ - Noetherian Rings的Ification
On the weakly Arf $(S_2)$-ifications of Noetherian rings
论文作者
论文摘要
虚弱的ARF $（s_2）$ - 可交换的Noetherian Ring $ r $的ification被认为是归一化旁边的典范扩展。 J. Lipman在1971年引入了$ r $的弱ARF财产（简称为wap），他的著名论文[12]，最近由[4]重新发现，并通过进一步的发展进行了密切探索。本文的目的是为了满足某些温和条件的给定的Noetherian Ring $ r $构建，这是满足WAP和条件$（S_2）Serre的最小模块 - 限制的birational Extension。我们将此扩展称为弱arf $（s_2）$ - ification，并开发基本理论，包括一些存在定理。
The weakly Arf $(S_2)$-ification of a commutative Noetherian ring $R$ is considered to be a birational extension which is good next to the normalization. The weakly Arf property (WAP for short) of $R$ was introduced in 1971 by J. Lipman with his famous paper [12], and recently rediscovered by [4], being closely explored with further developments. The present paper aims at constructing, for a given Noetherian ring $R$ which satisfies certain mild conditions, the smallest module-finite birational extension of $R$ which satisfies WAP and the condition $(S_2)$ of Serre. We shall call this extension the weakly Arf $(S_2)$-ification, and develop the basic theory, including some existence theorems.
